Woah...creepiness...I also discovered why it works (which took me about an hour XP) The doubling and halfing it basically means it turns into the same number. BUT you add 6 in between them. Because of this, there's an extra three. And since you subtract it with the same # you started with, it is three. ( I feel like a genius XD)
So...think of a number. double it. add 8. half it. subtract the # you start with. THe answer is FOUR. Right? (OH, sorry if it ruins the fun of magic numbers.)